600 - Non-negative Integers without Consecutive Ones.

Hard

Given a positive integer n, return the number of the integers in the range [0, n] whose binary representations do not contain consecutive ones.

Example 1:

Input: n = 5

Output: 5

Explanation:

Here are the non-negative integers <= 5 with their corresponding binary representations:
0 : 0
1 : 1
2 : 10
3 : 11
4 : 100
5 : 101
Among them, only integer 3 disobeys the rule (two consecutive ones) and the other 5 satisfy the rule.

Example 2:

Input: n = 1

Output: 2

Example 3:

Input: n = 2

Output: 3

Constraints:

• <code>1 <= n <= 10⁹</code>